Math Problem Statement

Исходя из данных рисунка, найди площадь трапеции ABCD. Даны: AB = 8, DC = 17, SB ⊥ (ABC).

Solution

The image you provided shows a trapezoid ABCDABCD with the following information:

  • AB=8AB = 8
  • DC=17DC = 17
  • SB(ABC)SB \perp (ABC), indicating a right angle between line SBSB and line ABCABC.

To find the area of trapezoid ABCDABCD, we need to know the height, which seems to be represented by SBSB. To calculate the area of a trapezoid, the formula is:

SABCD=12×(AB+DC)×hS_{ABCD} = \frac{1}{2} \times (AB + DC) \times h

Where:

  • ABAB is one of the parallel sides
  • DCDC is the other parallel side
  • hh is the height, which is the perpendicular distance between the parallel sides.

We need the height of the trapezoid. Could you provide that value or any additional information needed to find it?

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Math Problem Analysis

Mathematical Concepts

Geometry
Trapezoid Area Calculation
Perpendicular Height

Formulas

Area of trapezoid: S = 0.5 × (AB + DC) × h

Theorems

Properties of trapezoids
Perpendicular line theorem

Suitable Grade Level

Grades 8-10